Space-based clouds of atoms: Future gravitational wave detector

A horribly inaccurate artist representation of lasers in space. Still, lasers, in space!

Aurich Lawson / Thinkstock

I've always had a fascination with gravitational wave detection. Gravitational waves are the stretches and contractions in space-time that result from the motion of massive objects. The waves change the apparent distance between two objects as they pass through. But they are tiny—really tiny. To cope with the challenge of detecting something so tiny, gravitational wave observatories have become multi-decade projects that are worked on by large multinational teams. Each generation of sensor is more sensitive than the last, but nothing has been found yet.

In principle, it would have taken a fairly catastrophic event in our local neighborhood for the first detectors to see something. So it's only now that we are starting to reach sensitivities that might reasonably be expected to detect gravitational waves. The big problem is noise. Consider that the typical shift in length caused by a gravity wave is smaller than a hydrogen atom over a few kilometers, and you can see how simple mirror movements and noise in laser systems—lasers are key to making the measurement—could easily swamp the signal.

Maximizing the interference

The prototypical gravitational wave detector uses interferometry to detect very small changes in distance. At its most simple, interferometry consists of splitting a laser beam in two with a partial reflective mirror. The two beams are sent off in different directions and then returned to where they were split and interfere. If the distance that the two light beams traveled was exactly the same, then all the light is transmitted by the mirror where they were both split and interfered. If the distance between the two is different by a half wavelength, then all the light is reflected by the mirror.

The point is that we can balance our interferometer so that one path should always be dark. A photodetector placed on that arm will only click when a disturbance changes the length of one path relative to the other. With the right setup, this can be made extremely sensitive. The big reason for using this form of interferometer is to eliminate as much of the laser noise as possible. The key here is that, even if noise changes the laser wavelength just slightly, the same change is sent in both directions and the balance between transmitted and reflected light is unchanged.

But if you eliminate the laser noise in a different manner, you could use a simpler device. That is what this latest paper attempts to do, though I would argue that it is no simpler in the end.

Matter is better than light

The essential idea presented by the Stanford University physicists is to replace the light interferometer by a pair of matter interferometers. First, let's simplify the situation and just look at a single matter interferometer. Take a cold gas of atoms sitting in vacuum and hit them with a light pulse that we've tuned so that it should place them in an excited state. We also choose the energy and duration of the pulse such that the chance of exciting the atoms is around one half.

This puts the gas in a superposition of two states (the ground state and an excited state). Because the atoms have to absorb light to enter the excited state, they are also in a superposition state of stationary and are moving slowly through space since the absorption of light gives them a kick. After a delay, we hit the atoms with a second laser that has a slightly different frequency. This laser will only be absorbed by atoms that have been set in motion due to the first laser pulse. The effect of this laser is to return all the atoms to the ground state but leave them in a superposition of two different locations (a consequence of the superposition of their motion).

By a combination of these pulses, the gas of atoms can be split and sent along two paths and recombined. If nothing happens, we start with a blob of gas atoms and we end up with a blob of gas atoms. If, however, a gravitational wave passes through while the superposition of excited state and ground state exists, the excited atoms will feel like they have traveled further. When they recombine, the blob will have no atoms right at the center.

To make this really sensitive, you want the atoms to travel a fair distance before interfering, and you want to do this at two different locations and compare the results. But to do this, you would normally need two different sets of lasers, and the noise in the four independent laser systems will kill you.

The researchers have shown how to do this with a single pair of laser systems in such a way that the noise from each laser doesn't matter too much. Essentially, the laser that kicks the atoms into motion does so sequentially: it hits the first cloud and then later hits the second cloud, while the laser that de-excites them does so in reverse order. In doing this, the difference between the two matter interference patterns reflects the distance between the two atom interferometers. So when a gravitational wave passes through, the laser beams have to travel a little further or a little shorter to get from one cloud to the other, and we measure their arrival time to be a little different.

The atom interferometers act as very sensitive timers for this interval—if the laser pulse arrives at a different time, the atom interference pattern will change. So you could set up two atom interferometers at great distances as long as they can both be interrogated by the same pair of lasers. Then the interferometers will be sensitive to any gravity waves that alter the distance experienced by the light traveling between the two distant sites.

In which I oscillate between calling the authors geniuses and idiots

My initial reaction to the paper was that it is deeply flawed. After considering it for a few days, I'm sure that it isn't. Let's start with my reservations. The problem lies in using the atom interferometer to time the pulse. One major requirement for getting the interference to work is that the atoms have to stay in the excited state for quite a while (the sensitivity is proportional to that time). That means that the frequency of light that the atom will absorb is very precisely defined. This is also necessary because the second step is to de-excite the part of the cloud that is excited. But we can't make short pulses with such a narrow range of frequencies.

The challenge comes when you try to figure out when a light pulse arrives. Not only is there a fundamental limit to how short the pulse can be; the absorption of the light is also probabilistic. So the "arrival time" has an uncertainty that extends the entire width of the pulse. Indeed, it requires the entire light pulse to put the atomic cloud in the desired superposition state. There is a fundamental uncertainty in the timing, which, given the requirement for a very sharply defined laser frequency, would seem to doom this idea to failure.

What I had missed in my first read-through is that we are not talking about land-based gravitational wave observatories here. In space, this problem can be made to go away. Not being limited to a few kilometers, the two atom interferometers can be separated by vast distances, making this timing uncertainty very small relative to the total time traveled.

Once I understood that, I was convinced. Of course, there are huge technology hurdles between the idea and the implementation. For instance, the relative motion between the two satellites has to be tiny, yet the satellites also have to be separated by 1,000 or more kilometers and have a pair of lasers aimed at each other with high accuracy. The list goes on. Even so, it's a genius idea.

Not exactly: the major development here appears to be that they only need two satellites for this technique, not the three that LISA requires. Distance also appears to be much much smaller, only 1,000 km, instead of the millions that LISA needs (which could mean an Earth orbit will work, although there might be too many issues with noise from variations in Earth's gravitational field).

Given the nebulous understanding I have of lasers and excitations of atoms please slap me down if I'm being an idiot. That said:

My understanding is that it's impossible to naturally promote more than half a population of atoms into a higher state. At saturation (50%) the probabilities of a photon hitting a ground state atom would be the same as for the higher state. The ground state atom will be promoted but the atom already in the higher state would release the stored energy as another photon and return to ground state. Yes?

If my explanation above is correct I suppose the laser pulses we're talking about here must be sufficiently short such that there is no chance of demoting atoms that have gone into a higher energy state? Otherwise you'd have ground state atoms moving along with (or possibly faster than) the promoted atoms.

One thing I don't understand: you say "the relative motion between the two satellites has to be tiny, yet the satellites also have to be separated by 1,000 or more kilometers" --these requirements seem to me to be mutually exclusive.

Even if the distance between the two satellites is kept to exactly 1000 km (for example), the two satellites, which are presumably in the same orbit, are at different portions of the orbit and are therefore traveling in different directions. So although the distance doesn't change, there are large relative motions.

One thing I don't understand: you say "the relative motion between the two satellites has to be tiny, yet the satellites also have to be separated by 1,000 or more kilometers" --these requirements seem to me to be mutually exclusive.

Even if the distance between the two satellites is kept to exactly 1000 km (for example), the two satellites, which are presumably in the same orbit, are at different portions of the orbit and are therefore traveling in different directions. So although the distance doesn't change, there are large relative motions.

"relative motion" in this case is referring to the motion of satellite A relative to the position of satellite B, not the motion of satellites A & B relative to the position of the Earth.

Not exactly: the major development here appears to be that they only need two satellites for this technique, not the three that LISA requires. Distance also appears to be much much smaller, only 1,000 km, instead of the millions that LISA needs (which could mean an Earth orbit will work, although there might be too many issues with noise from variations in Earth's gravitational field).

LISA is defunct since NASA pulled out its funding. The LISA mission lives on as eLISA, with ESA (European Space Association)'s funding only. The collaboration hope to launch a test mission called LISA Pathfinder in 2014 to make sure the technologies developed for the original LISA mission work as intended. The next step is then to apply for funding for an ESA L2 or L3 launch spot, which would put the eventual three-satellite project on path for a launch in 2028 or 2034.

You can read the white paper in support of the L2/L3 application here.

Given the nebulous understanding I have of lasers and excitations of atoms please slap me down if I'm being an idiot. That said:

My understanding is that it's impossible to naturally promote more than half a population of atoms into a higher state. At saturation (50%) the probabilities of a photon hitting a ground state atom would be the same as for the higher state. The ground state atom will be promoted but the atom already in the higher state would release the stored energy as another photon and return to ground state. Yes?

If my explanation above is correct I suppose the laser pulses we're talking about here must be sufficiently short such that there is no chance of demoting atoms that have gone into a higher energy state? Otherwise you'd have ground state atoms moving along with (or possibly faster than) the promoted atoms.

The second statement sums it up, but it is a little more complicated (and way cooler) than that. You can put all the atoms in a population in the excited state, but it requires that the pulse energy/time of the pulse is carefully controlled. First, the energy has to arrive in a time that is shorter than the lifetime of the excited state (actually shorter than the coherence lifetime of the excited state). Then, the total energy has to be right. We usually talk about this as pulse area. If the pulse area is pi, then you will put half the atoms in the excited state. But, if the area is 2pi, then you will cycle them right back to the ground state again. Using this, you can create any superposition between excited state and ground state that you desire.

Given the nebulous understanding I have of lasers and excitations of atoms please slap me down if I'm being an idiot. That said:

My understanding is that it's impossible to naturally promote more than half a population of atoms into a higher state. At saturation (50%) the probabilities of a photon hitting a ground state atom would be the same as for the higher state. The ground state atom will be promoted but the atom already in the higher state would release the stored energy as another photon and return to ground state. Yes?

If my explanation above is correct I suppose the laser pulses we're talking about here must be sufficiently short such that there is no chance of demoting atoms that have gone into a higher energy state? Otherwise you'd have ground state atoms moving along with (or possibly faster than) the promoted atoms.

The second statement sums it up, but it is a little more complicated (and way cooler) than that. You can put all the atoms in a population in the excited state, but it requires that the pulse energy/time of the pulse is carefully controlled. First, the energy has to arrive in a time that is shorter than the lifetime of the excited state (actually shorter than the coherence lifetime of the excited state). Then, the total energy has to be right. We usually talk about this as pulse area. If the pulse area is pi, then you will put half the atoms in the excited state. But, if the area is 2pi, then you will cycle them right back to the ground state again. Using this, you can create any superposition between excited state and ground state that you desire.

Uh oh...

"coherence lifetime" -> quantum -> run away!!!

Too late.

***brain pops***

However, thanks for trying to explain it to a super layman. I'll take your word that it's more complicated and WAY cooler.

Are there any (presumably tiny) time dilation effects to consider? I assume it takes a small but finite amount of time for an atom to absorb a photon, so would that be perturbed by a gravitational wave along with the location of the atom? And what about the orbits of the two laser satellites -- wouldn't they have to be in exactly the same gravitational reference frame (with respect to the Earth-Moon system)?

I'm not expert on relativity or QM and my morning coffee has long worn off, so apologies if these questions are silly.

Are there any (presumably tiny) time dilation effects to consider? I assume it takes a small but finite amount of time for an atom to absorb a photon, so would that be perturbed by a gravitational wave along with the location of the atom? And what about the orbits of the two laser satellites -- wouldn't they have to be in exactly the same gravitational reference frame (with respect to the Earth-Moon system)?

I'm not expert on relativity or QM and my morning coffee has long worn off, so apologies if these questions are silly.

Gravitational waves travel at the speed of light. They're distortions in the very fabric of spacetime. Both spacecraft cannot be in the same reference frame in the presence of a gravitational wave, because, by definition, the gravitational wave has changed the reference with respect to each object. It's the change in reference frame which can be used to detect the gravitational wave, in this instance the (lack of) absorption of photons in atoms.

I'm not sure about your first question but I think the absorption is instantaneous. Besides, gravitational waves travel at the speed of light so there is no 'length contraction' or 'time dilation' traditionally associated with massive objects (special relativity). I'm not an astronomer though so I welcome corrections from someone wiser!

Articles like this tell me how much the scientists were bullshitting back in the mid 90's. They said they could build machines to detect gravity waves back then! Yet even today we don't have the sensitivity.

Articles like this tell me how much the scientists were bullshitting back in the mid 90's. They said they could build machines to detect gravity waves back then! Yet even today we don't have the sensitivity.

It was only once the scientists built the first generation of detectors that they realised that there was so much noise arising from thermal effects such as coatings on mirrors. Coating thermal noise is the limiting factor at detectors' (Michelson interferometers) most sensitive frequencies. This noise swamps all but the biggest signals, which is what the article alludes to. The first generation of detectors were therefore only sensitive to supernovae in the local galaxy, which occur only once or twice per century.

The second generation of detectors are being assembled now, and the third generation is in planning. Scientists have improved the noise performance of the detectors significantly since the first generation, through a combination of different materials (with lower Brownian and coating thermal noise), more and better suspensions (for ground vibration isolation) and signal enhancement techniques (such as squeezing, as linked to in the article, signal recycling, power recycling, variational readout, etc).

If the second generation detectors perform to their design specification, it should be possible to detect gravitational waves on a daily/weekly basis. However, detection of the first gravitational wave is only the beginning of the story. During astronomical events such as black hole formation, photons cannot be used to 'look inside' because they can't escape. Gravitational waves can escape, and can be used to characterise the bodies (along with neutrinos, which might also escape). This 'multi messenger astronomy' can be used to study the universe in greater detail.

Gravitational waves have never been detected. They are theoretical. I find it really disappointing the article discussed them as if they are a known, factual thing. And even more disappointed nobody has pointed that out.

Gravitational waves have never been detected. They are theoretical. I find it really disappointing the article discussed them as if they are a known, factual thing. And even more disappointed nobody has pointed that out.

The very fact that we are trying to detect them implies there theoretical. But on the other hand they ARE directly predicted by Einstein theory, and has that ever been wrong?

Chris Lee / Chris writes for Ars Technica's science section. A physicist by day and science writer by night, he specializes in quantum physics and optics. He lives and works in Eindhoven, the Netherlands.